Method of receiver processing of CDMA signals in a CDMA system

ABSTRACT

The method of receiver processing of CDMA signals in a CDMA system includes first converting a received signal in the time domain to a received signal in the frequency domain, and equalizing the received signal in the frequency domain using a set of frequency domain weights. The equalized received signal in the frequency domain is converted to an equalized received signal in the time domain. The set of frequency domain weights are adaptively adjusted at a symbol rate of the received signal in the time domain based on an error signal produced from the received signal in the frequency domain and a frequency domain representation of a known pilot signal of the CDMA system.

BACKGROUND OF THE INVENTION

In the code-division multiple access (CDMA) downlink (base station tomobile station communication link), equalization can restore theorthogonality lost in multipath channels, and exceed the performanceattained by a Rake receiver. For practical implementation of theequalizers, two forms of an adaptive least-mean-square (LMS) algorithmhave been proposed. Both forms operate on the individual received chips,however, the straightforward LMS algorithm updates the weights at everychip time, whereas the second approach (called “LMS-G”) performs anextra correlation at the equalizer output and updates the weights at thesymbol rate. It has also been shown that with careful adjustment of theLMS step size, μ, the LMS-G algorithm is superior for both SISO (singleinput single output) and MIMO (multiple input multiple output)equalizers.

Unfortunately, the adaptive algorithms have fairly high complexity inthe MIMO case, due to the large number (M N) of parallel filtersrequired (where M is the number of transmit antennas and N the number ofreceive antennas in the MIMO system). The convergence time of the LMS-Galgorithm for the channels of interest is 3 msec (for a 4×4 equalizer onthe TU (Typical Urban) channel) which restricts its use to slowly movingmobile terminals.

Application of LMS algorithm in the frequency domain for a SISO TDMA(time division multiple access) system has also been proposed. Thisso-called FLMS (frequency LMS) algorithm operates in a block mode, usingeither overlap-add or overlap-save to perform the time domain linearconvolutions. FLMS can be both less complex than ordinary LMS and offerfaster convergence when an individual step-size is chosen for eachfrequency bin. The so-called TLMS (transform domain LMS) algorithmsoperate in a sample-by-sample mode and have substantially greatercomplexity than FLMS.

SUMMARY OF THE INVENTION

According to the present invention, the block mode FLMS algorithm usingoverlap-save has been adapted for use in a CDMA system by extending thealgorithm to include an extra correlator on the pilot code or signal.This new algorithm may be referred to as FLMS-G. Namely, the FLMSalgorithm is trained and converged using the known pilot signal of theCDMA system. This permits adaptive adjustment of the FLMS set offrequency domain weights at the symbol rate of the equalized signal.Additionally, according to the present invention, the new FLMS-G isfurther modified for application to MIMO transmission and reception.

The present invention further provides a significant reduction inconvergence time, particularly, for MIMO equalizers when the step sizematrix of the FLMS algorithm is generalized to include termscorresponding to the spatial cross-spectrums.

According to one embodiment of the present invention, a method ofreceiver processing of CDMA signals in a CDMA system includes firstconverting a received signal in the time domain to a received signal inthe frequency domain, and equalizing the received signal in thefrequency domain using a set of frequency domain weights. The equalizedreceived signal in the frequency domain is converted to an equalizedreceived signal in the time domain. The set of frequency domain weightsare adaptively adjusted at a symbol rate of the received signal in thetime domain based on an error signal produced from the received signalin the frequency domain and a frequency domain representation of a knownpilot signal of the CDMA system.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given herein below and the accompanying drawings,wherein like elements are represented by like reference numerals, whichare given by way of illustration only and thus are not limiting of thepresent invention and wherein:

FIG. 1 illustrates a single-input single-output implementation of themethod of receiver processing of CDMA signals according to an embodimentof the present invention; and

FIG. 2 illustrates a multiple-input multiple-output implementation ofthe method of receiver processing of CDMA signals according to anembodiment of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

To better understand the present invention, the time domain version ofthe LMS-G algorithm will be reviewed, followed by an explanation of thederivation for the FLMS-G algorithm according to the present invention.Then SISO and MIMO equalizer implementations of the new FLMS-G algorithmaccording to the present invention will be described.

Review of LMS-G Algorithm

As discussed above, a time domain chip-level equalizer followed by anadditional pilot-channel correlator, which updates at the symbol rate,has been proposed. This LMS-G algorithm has also been used for the MIMOCDMA case with code re-use across antennas. In this section, this(time-domain) LMS-G algorithm, for SISO and for MIMO channels, will bebriefly reviewed.

The equalizer output the k-th chip is y_(k)=r_(k) ^(T)w_(j), where r_(k)is the received vector and w_(j) the equalizer weight vector asexpressed below,r _(k) =[r(k−E+1), . . . , r(k−1),r(k)]^(T)w _(j) =[w(0), w(1), . . . , w(E−1)]^(T)   (2.1)and where the equalizer length is E chips. Note that j is an index forthe equalizer updates, which occurs at a multiple of the symbol rate,j=└(k+1)/(BG)┘, where G is the number of chips per symbol, and B is thenumber of pilot symbols per update. For simplicity, assume E=BG.

The equalizer output is despread with B consecutive pilot symbols. Thedespreader output at time j is a_(j)=p_(j) ^(H)R_(j)w_(j), wherep _(j) =[p(k−d), p(k−d+1), . . . , p(k−d+BG−1))]^(T)R _(j) =[r _(k+BG-1) r _(k+BG-2) . . . r _(k+BG-E]) _(BG×E)   (2.2)

Here, p(k) denotes the pilot chip at time k, and 0≦d<E−1 is a delay thata system designer is free to choose. The error at the j-th update isdefined as,e _(j) =a _(j) −BGA _(p)   2.21where A_(p) is the amplitude of the pilot signal. Defining the costfunction J=∥e_(j)∥² and taking the derivative w.r.t. w_(j), the LMS-Galgorithm is derived as,w _(j−1) =w _(j) +μR _(j) ^(H) p _(j) [GA _(p) −a _(j)]  (2.3)where μ is the (scalar) LMS step-size.

This basic procedure can be extended to MIMO channels. A separateequalizer is used for each of the M transmitters (nothing is gained by a“joint” procedure that uses all M pilots simultaneously). The N FIRfilters (one per receive antenna) making the equalizer are,w_(j)=[w_(m,1) ^(T), w_(m,2) ^(T), . . . , w_(m,N) ^(T)]whose subcomponents are analogous to equation (2.1). Then the receivedsignal is grouped into,R_(j)=[R_(1,j),R_(2,j), . . . , R_(N,j)]where each subcomponent is analogous to equation (2.2) for each receiveantenna. The MIMO LMS-G algorithm is again given by (2.3), where them-th pilot signal is used in p_(j).Derivation of FLMA-G Algorithm

To derive the new FLMS-G procedure according to the present inventionfor SISO channels, note that the terms R_(j) ^(H)p_(j) and R_(j)w_(j)correspond to linear convolutions, which may be converted to circularconvolutions by “embedding” them in circulant matrices, e.g.,$\begin{matrix}{C\overset{\Delta}{=}\left\lbrack \quad\begin{matrix}{r\left( {k + {BG} - {2E}} \right)} & {r\left( {k + {BG} - {2E} - 1} \right)} & \ldots & \quad & {r\left( {k + {BG} - {2E} + 1} \right)} \\\vdots & {r\left( {k + {BG} - {2E}} \right)} & ⋰ & \quad & {r\left( {k + {BG} - {2E} + 2} \right)} \\{r\left( {k - 1} \right)} & \vdots & ⋰ & ⋰ & ⋰ \\{r(k)} & {r\left( {k - 1} \right)} & ⋰ & ⋰ & ⋰ \\\vdots & {r(k)} & ⋰ & ⋰ & {r\left( {k + {BG} - 1} \right)} \\{r\left( {k + {BG} - 1} \right)} & \vdots & ⋰ & ⋰ & {r\left( {k + {BG} - {2E}} \right)}\end{matrix} \right\rbrack} & (3.1)\end{matrix}$

The lower left quadrant of this circulant matrix is identical to R_(j)in equation (2.2). The last row of matrix C is obtained from R_(j)beginning in the lower left corner and moving right along the last row,collecting samples in reverse-time order until reaching r(k+BG−2E). Eachhigher row of C is the left circular shift of the preceding row. Theselinear convolutions may be efficiently implemented by taking the FFT ofthe first column C (denoted c₁) and computing, $\begin{matrix}{{{IFFT}\left\{ {{FFT}{\left\{ \left\lbrack c_{1} \right\rbrack \right\} \odot {FFT}}\left\{ \begin{bmatrix}w \\0\end{bmatrix} \right\}} \right\}} = \begin{bmatrix}{skip} \\{save}\end{bmatrix}} & (3.2)\end{matrix}$

The symbol ⊙ denotes “element-by-element” multiplication. The “save”output of equation (3.2) corresponds to R_(j)w_(j). Similar reasoninggives an expression for R_(j) ^(H)p_(j), however, it is necessary totake the conjugate of the result.

For frequency-domain equalization according to the present invention,the scalar step-size, μ, in equation (2.3) may be generalized to adiagonal matrix D_(j) whose elements are computed adaptively as,D_(l)=μP_(j) ⁻¹P _(j)=(1−β)P _(j−1)+β diag(|FFT{r _(j−1)}|²)   (3.3)where diag (•) denotes a diagonal matrix, the norm is taken per-element,and β is a forgetting factor set by the system designer based onempirical study (e.g., the forgetting factor may have a value of 0.05).This generalization is responsible for the improved convergence speed ofFLMS-G.

According to one exemplary embodiment, FLMS-G receiver processing ofCDMA signals according to the present invention includes the steps of:

-   1) Get new (non-overlapping) input vector, r_(j).    ${\left. 2 \right)\quad y_{j}} = \begin{bmatrix}    r_{j - 1} \\    r_{j}    \end{bmatrix}$    3) {overscore (y)} _(j) =FFT(y _(j))    4) {overscore (z)} _(j) ={overscore (y)} _(j) ⊙{overscore (w)} _(j)    5) z _(j) =IFFT({overscore (z)} _(j)), and z _(j) =z _(j)(E+1:2E)    6) e _(j) =GA _(p) −p _(j) ,z _(j)    ${\left. 7 \right)\quad p_{k}^{\prime}} = \begin{bmatrix}    0_{E \times 1} \\    p_{k}    \end{bmatrix}$    8) {overscore (g)} _(j) =e _(j)(conj({overscore (y)})_(j) ⊙FFT(p    _(j)))    10) D _(j) =μP _(j) ⁻¹ ,P _(j)=(1−β)P _(j−1)+β diag(|{overscore (y)}    _(k)|²)    11) {overscore (w)}_(j+1) ={overscore (w)} _(j) +D _(j) {overscore    (g)} _(j)-   12) next j, go to 1).

The FLMS-G receiver processing method described above requires 3 FFToperations per update (each of length 2E) .

The extension to MIMO is straightforward, as was shown above for LMS-G.A beneficial simplification results from summing the spatial filters inthe frequency-domain, drastically reducing the number of IFFTs needed.Following equation (3.3), the MIMO step size matrix is diagonal, withelements that correspond to the power spectrum of the signals receivedon each of the N antennas. This will be described in detail in the nextsection below.

Improvement Using Cross-Spectrum

By analogy to the recursive-least-squares (RLS) algorithm, we can seethat the “optimal” step size matrix is the inverse of the completecovariance matrix,R_(opt)=E{{overscore (y)}{overscore (y)}^(H),{overscore (y)}=[{overscore (y)}₁ ^(T), . . . , {overscore (y)}₁ ^(T), .. . , {overscore (y)}_(N) ^(T)]^(t), and this may be approximated bytaking only the diagonal elements so the resulting matrix is easy toinvert. In the previous sections, the subscript index represented a timeindex. However, in this section and the equation given below, thesubscript index represent an index on the number of receive antennas N.A better approximation results if the cross-spectrum terms are alsoincluded, leading to an über-matrix of diagonal matrices as shown inequation 4.1 below. $\begin{matrix}{{{\overset{¨}{U}D} = \begin{bmatrix}P_{1,1} & P_{1,2} & \ldots & P_{1,N} \\P_{1,2}^{*} & P_{2,2} & \quad & \quad \\\quad & \quad & ⋰ & \vdots \\P_{1,2}^{*} & P_{2,N}^{*} & \ldots & p_{N,N}\end{bmatrix}}{{P_{i,n}\left( {j + 1} \right)} = {{\left( {1 - \beta} \right)\quad P_{i,n}\quad(j)} + {\beta\quad{diag}\quad\left( {{\overset{\_}{y}}_{i} \odot {\overset{\_}{y}}_{n}} \right)}}}} & (4.1)\end{matrix}$where N is the number of receive antennas and indices i and n each indexa particular receive antenna.

The improved step size matrix is then D=μ(ÜD)⁻¹. The structure of the ÜDmatrix makes it easy to invert.

SISO Implementation of FLMS-G

Next, a SISO implementation of FLMS-G will be described with respect toFIG. 1. For purposes of explanation, the same variables as used in theabove described equations will be used in this description. As shown, Enew chips r_(j) and E old chips r_(j−1) of a signal received over anantenna (represented as $\left. {y_{j} = \begin{bmatrix}r_{j - 1} \\r_{j}\end{bmatrix}} \right)$are converted to the frequency domain by a first converter 10. A firstmultiplier 12 obtains the product {overscore (z)}_(j) between thereceived signal {overscore (y)}_(j) in the frequency domain and the setof frequency domain weights {overscore (w)}_(j) to produce the equalizedreceived signal in the frequency domain.

A second converter 14 converts the signal {overscore (z)}_(j) to thetime domain. A second of the E chips in the time domain dot productserve as the equalized received signal that is output by the equalizer.The inner product or dot product of this equalized received signal andthe chips of the known pilot signal for the CDMA system is obtained by asecond multiplier 16. The output of the second multiplier 16 results inan estimate of a pilot symbol amplitude from the equalized receivedsignal in the time domain.

A subtractor 18 subtracts the amplitude of the pilot signal GA_(p) fromthe output of the second multiplier 16. An inverter 20 inverts theoutput of the subtractor 18 to produce a scalar that represents adifference in amplitude between the estimated pilot symbol amplitude anda known amplitude of the known pilot signal in the CDMA system.

A third converter 22 obtains the conjugate of the output from the firstconverter 10, and a fourth converter 24 converts E zero chips and Echips of the known pilot signal to the frequency domain. A thirdmultiplier 26 mixes this frequency domain version of the pilot signalwith the conjugate of the output from the first converter 10. Theresulting output indicates a direction of an error in the equalization.The output of the inverter 20 provides the magnitude of this error. Afourth multiplier 28 combines the two to obtain the errorsignal{overscore (g)}_(j).

A step matrix calculator 30 generates the diagonal matrix D_(j)according to equation 3.3. A fifth multiplier 32 multiplies thisdiagonal matrix and error signal. This affects the error signal per tone(i.e., frequency), so that the error signal from weak tones may beboosted. An adder 34 adds the output of the fifth multiplier 32 andoutput of the fifth multiplier delayed by a delay 36 to generate the setof frequency domain weights.

MIMO Implementation of FLMS-G

Next, a MIMO implementation of FLMS-G will be described with respect toFIG. 2. It will be understood that a MIMO system involves transmissionof a plurality, M, of signals from one location using multiple transmitantennas, and receipt of these signals using a plurality of receiveantennas at a second location. A MIMO system includes a pilot signal foreach of the M transmit antennas. FIG. 2 illustrates the structure forreceiver processing using one of the pilot signals. As will beappreciated, the structure for converting the received signals to thefrequency domain is common for each pilot signal, and the structure forgenerating and applying the sets of frequency domain weights isduplicated for each of the respective pilot signals. This latterstructure also generates equalized output associated with eachtransmitted signal. Namely, the M equalized outputs have been temporallycorrected and spatially separated by this structure to approximate the Mtransmitted signals.

The structure for generating and applying the sets of frequency domainweights includes a first set of multipliers 50. Each multiplier in thefirst set of multipliers 50 multiplies a respective one of the receivedsignals in the frequency domain by a respective set of frequency domainweights. An adder 52 adds the output of each multiplier in the first setof multipliers 50. From the output of the adder 52, the equalizedreceived signal and the magnitude of the error signal are produced inthe same manner described above with respect to FIG. 1.

Each converter in a set of converters 54 obtains the conjugate of arespective received signal in the frequency domain, and a converter 24converts E zero chips and E chips of the pilot signal associated withthis structure to the frequency domain (in this case the pilot signal ofthe mth transmit antenna). A second set of multipliers 56 mixes thisfrequency domain version of the pilot signal with each conjugate of theoutput from the set of converters 54. The resulting outputs eachindicate a direction of an error in the equalization. The output of theinverter 20 provides the magnitude of this error. Each multiplier in athird set of multipliers 58 combines the output from a respective one ofthe third set of multipliers 56 and the output of the inverter 20 togenerate an error signal.

An uber matrix calculator 60 generates a set of power-spectra andcross-power spectra are generated by multiplying all pairs of receivedfrequency-domain inputs and talking time averages (see eqn 4.1 ). Theindividual spectra are arranged as diagonal matrices, and then an“uber-diagonal” matrix is formed. The uber matrix calculator 60 producesthe inverse of the uber-diagonal matrix as the step-size matrix, appliesthis to a matrix multiplier 62. The matrix multiplier 62 performs matrixmultiplication between the step size matrix and the respective errorsignals. This affects each error signals per tone (i.e., frequency), sothat the error signal from weak tones may be boosted. As will beappreciated, the matrix multiplication produces an output vector foreach error signal. Each adder in a set of adders 64 adds a respectiveoutput from the matrix multiplier 62 and the respective output of thematrix multiplier 62 delayed by a respective delay in a set of delays 66to generate a set of frequency domain weights.

The method and apparatuses according to the present inventionsignificantly reduce the complexity of the equalization process byperforming operations in the frequency domain. This is particularly truewith a MIMO CDMA system. Furthermore, the uber-diagonal matrix of thepresent invention provides for improved convergence time, againparticularly with a MIMO CDMA system.

The invention being thus described, it will be obvious that the same maybe varied in many ways. For example, using FFT operations of length 2Echips and performing the skip/save operation may not be strictlynecessary. Instead, only the current E chips of the received signal maybe used (with a corresponding decrease in the number of chips in theother operations as well). Such variations are not to be regarded as adeparture from the invention, and all such modifications are intended tobe included within the scope of the invention.

1. A method of receiver processing of CDMA signals in a CDMA system,comprising: first converting a received signal in the time domain to areceived signal in the frequency domain; equalizing the received signalin the frequency domain using a set of frequency domain weights; secondconverting the equalized received signal in the frequency domain to anequalized received signal in the time domain; adaptively adjusting theset of frequency domain weights at a symbol rate of the received signalin the time domain based on an error signal produced from the receivedsignal in the frequency domain and a frequency domain representation ofa known pilot signal of the CDMA system.
 2. The method of claim 1,wherein the adaptively adjusting step comprises: generating the errorsignal in the frequency domain to represent a difference of theequalized received signal from the known pilot signal; and applying astep size matrix to the error signal to generate the set of frequencydomain weights, the step size matrix providing a respective amount toadjust each weight of the set of frequency domain weights based on aspectrum of received signal in the frequency domain.
 3. The method ofclaim 2, wherein the generating step comprises: estimating a pilotsymbol amplitude from the equalized received signal in the time domain;determining a difference in amplitude between the estimated pilot symbolamplitude and a known amplitude of the known pilot signal as an errormagnitude; multiplying the received signal in the frequency domain bythe known pilot signal in the frequency domain to obtain an errordirection; and multiplying the error magnitude and the error directionto obtain the error signal.
 4. The method of claim 3, furthercomprising: determining the step size matrix according to the followingexpression,D_(l)=μP_(j) ⁻¹P _(j)=(1−β)P _(j−1)+β diag(|FFT{r _(j−1)}|²)   (3.3) where r is thereceived signal in the time domain, diag (•) denotes a diagonal matrix,and β is a forgetting factor constant.
 5. The method of claim 2, furthercomprising: determining the step size matrix according to the followingexpression,D_(l)=μP_(j) ⁻¹P _(j)=(1−β)P _(j−1)+β diag(|FFT{r _(j−1)}|²)   (3.3) where r is thereceived signal in the time domain, diag (•) denotes a diagonal matrix,and β is a forgetting factor constant.
 6. The method of claim 1, whereinthe first converting step converts a vector yj of a received signal rjand the previous received signal rj−1 where ${y_{j} = \begin{bmatrix}r_{j - 1} \\r_{j}\end{bmatrix}},$ each of the received signal rj and the previousreceived signal rj−1 having E elements; the equalizing step calculates aproduct of the vector yj and the set of weights to generate a vector zhaving 2E elements; and the second converting step converts a second Eof the 2E elements in the vector z to the time domain.
 7. The method ofclaim 6, wherein the adaptively generating step comprises: generatingthe error signal {overscore (g)}_(j) in the frequency domain torepresent a difference of the equalized received signal from the knownpilot signal according to the following expression,${\overset{\_}{g}}_{j} = {e_{j}\left( {{{conj}\left( \overset{\_}{y} \right)}_{j} \odot {{FFT}\left( p_{j}^{\prime} \right)}} \right)}$where $\begin{matrix}{{e_{j} = {{GA}_{p} - \left\langle {p_{j},z_{j}} \right\rangle}},} \\{{p_{k}^{\prime} = \begin{bmatrix}0_{E \times 1} \\p_{k}\end{bmatrix}},}\end{matrix}$ and p_(k) represents the known pilot signal,

p_(j),z_(j)

represents the conventional dot product or an accumulation of chips forone symbol in the equalized received signal in the time domain, andGA_(p) represents a magnitude of the known pilot signal; and applying astep size matrix Dj to the error signal to generate the set of frequencydomain weights, the step size matrix providing a respective amount toadjust each weight of the set of frequency domain weights based on aspectrum of received signal in the frequency domain.
 8. The method ofclaim 7, further comprising: determining the step size matrix Djaccording to the following expression,D_(l)=μP_(j) ⁻¹P _(j)=(1−β)P _(j−1)+β diag(|FFT{r _(j−1)}|²)   (3.3) where r is thereceived signal in the time domain, diag (•) denotes a diagonal matrix,and β is a forgetting factor constant.
 9. The method of claim 1, whereinthe CDMA system is a multiple-input multiple-output (MIMO) CDMA systemhaving a known pilot signal associated with each transmit antenna; thefirst converting step converts a plurality of received signals in thetime domain to received signals in the frequency domain; and for eachknown pilot signal, the equalizing step equalizes the received signalsin the frequency domain using a set of frequency domain weightsassociated with each received signal; and the method further includes,combining the equalized received signals; and wherein the secondconverting step converts the combined equalized received signal in thefrequency domain to a combined equalized received signal in the timedomain; and the adaptively adjusting step adaptively adjusts the set offrequency domain weights associated with each received signal at asymbol rate of the received signal in the time domain based on an errorsignal produced from the received signal in the frequency domain and afrequency domain representation of the known pilot signal.
 10. Themethod of claim 9, wherein, for each known pilot signal, the adaptivelyadjusting step comprises: generating the error signal associated witheach received signal; and applying a step size matrix to the errorsignal to generate the set of frequency domain weights, the step sizematrix providing a respective amount to adjust each weight of the set offrequency domain weights based on a spectrum of received signal in thefrequency domain.
 11. The method of claim 10, wherein the applying stepcomprises: determining the step size matrix D as,${D = {\mu\left( {\overset{¨}{U}D} \right)}^{- 1}},{where}$${\overset{¨}{U}D} = \begin{bmatrix}P_{1,1} & P_{1,2} & \ldots & P_{1,N} \\P_{1,2}^{*} & P_{2,2} & \quad & \quad \\\quad & \quad & ⋰ & \vdots \\P_{1,2}^{*} & P_{2,N}^{*} & \ldots & p_{N,N}\end{bmatrix}$${P_{i,n}\left( {j + 1} \right)} = {{\left( {1 - \beta} \right)\quad P_{i,n}\quad(j)} + {\beta\quad{diag}\quad\left( {{\overset{\_}{y}}_{i} \odot {\overset{\_}{y}}_{n}} \right)}}$where N is the number of receive antennas, indices i and n each index aparticular receive antenna, for an antenna j,${{\overset{\_}{y}}_{j} = {{FFT}\left( y_{j} \right)}},\quad{y_{j} = \begin{bmatrix}r_{j - 1} \\r_{j}\end{bmatrix}}$ r_(j) is a current received signal in the time domainand r_(j−1) is a previous received signal in the time domain, diag (•)denotes a diagonal matrix, and β is a forgetting factor constant.
 12. Amethod of receiver processing of CDMA signals in a CDMA system,comprising: applying an LMS (least mean squares) algorithm to a receivedCDMA signal in the frequency domain where weights of the LMS algorithmare updated in the frequency domain at a symbol rate of the receivedCDMA signal.
 13. The method of claim 12, wherein the applying stepapplies the LMS algorithm trained using a know pilot signal of the CDMAsystem.
 14. The method of claim 12, wherein a step size adjustment ofthe LMS algorithm is preformed using step size matrix providing arespective amount to adjust each weight of the set of frequency domainweights based on a spectrum of received signal in the frequency domain.